Route information processing apparatus and route information processing method

ABSTRACT

A route information processing apparatus includes: a processor configured to execute a program; and a memory configured to store the program, wherein, based on the program, the processor performs operations to: calculate maximum values corresponding to a Frechet distance between one line segment of one or more line segments between observation points included in a trajectory and each of sets of two nodes corresponding to the one line segment, the nodes being included in a route graph including linked paths which link nodes; and acquire a path corresponding to the trajectory having a smallest value among the maximum values of the one or more line segments.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based upon and claims the benefit of priority of theprior Japanese Patent Application No. 2014-246250, filed on Dec. 4,2014, the entire contents of which are incorporated herein by reference.

FIELD

The embodiment discussed herein is related to a route informationprocessing apparatus and a route information processing method.

BACKGROUND

In spatial information analysis, the analysis of the route of a movablebody is performed.

Japanese Laid-open Patent Publication No. 2004-325083 or H. Alt, A.Efrat, G. Rote, and C. Wenk, “Matching planar maps”, J. Algorithms 49,262-283, 2003 discloses related art.

SUMMARY

According to an aspect of the embodiments, a route informationprocessing apparatus includes: a processor configured to execute aprogram; and a memory configured to store the program, wherein, based onthe program, the processor performs operations to: calculate maximumvalues corresponding to a Frechet distance between one line segment ofone or more line segments between observation points included in atrajectory and each of sets of two nodes corresponding to the one linesegment, the nodes being included in a route graph including linkedpaths which link nodes; and acquire a path corresponding to thetrajectory having a smallest value among the maximum values of the oneor more line segments.

The object and advantages of the invention will be realized and attainedby means of the elements and combinations particularly pointed out inthe claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory and arenot restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates an example of a route information processing system;

FIG. 2 illustrates an example of trajectory data;

FIG. 3 illustrates an example of a route graph;

FIG. 4 illustrates an example of a trajectory and an example of a routegraph;

FIG. 5 illustrates an example of a correspondence between a line segmentbetween observation points on a trajectory and a node on a route graph;

FIGS. 6A and 6B illustrate an example of a correspondence between a linesegment between observation points on a trajectory and a node on a routegraph;

FIG. 7 illustrates an example of a correspondence between a line segmentbetween observation points on a trajectory and a node on a route graphat the time of updating;

FIG. 8 illustrates an example of a matrix;

FIG. 9 illustrates an example of a shortest distance between a node anda line segment;

FIGS. 10A, 10B, and 10C illustrate an example of a method of calculatinga Frechet distance;

FIG. 11 illustrates an example of a method of calculating a Frechetdistance;

FIG. 12 illustrates an example of a computer;

FIG. 13 illustrates an example of a route information process;

FIG. 14 illustrates an example of a trajectory and an example of a routegraph;

FIG. 15 illustrates an example of a number of a line segment;

FIG. 16 illustrates an example of a distance calculation process;

FIG. 17 illustrates an example of an initial distance calculationprocess;

FIG. 18 illustrates an example of an initial distance calculationprocess;

FIG. 19 illustrates an example of an initial distance calculationprocess;

FIG. 20 illustrates an example of a list Q and an example of a list Lafter an initial distance calculation process;

FIG. 21 illustrates an example of extraction of target processing datain a first loop;

FIG. 22 illustrates an example of a second-stage distance calculationprocess;

FIG. 23 illustrates an example of a second-stage distance calculationprocess;

FIG. 24 illustrates an example of a second-stage distance calculationprocess;

FIG. 25 illustrates an example of a list;

FIG. 26 illustrates an example of a list;

FIG. 27 illustrates an example of a list;

FIG. 28 illustrates an example of a list;

FIG. 29 illustrates an example of a list;

FIG. 30 illustrates an example of a list;

FIG. 31 illustrates an example of a list;

FIG. 32 illustrates an example of a list;

FIG. 33 illustrates an example of a list;

FIG. 34 illustrates an example of a list;

FIG. 35 illustrates an example of a list;

FIG. 36 illustrates an example of a list;

FIG. 37 illustrates an example of a list;

FIG. 38 illustrates an example of a list;

FIG. 39 illustrates an example of a list;

FIG. 40 illustrates exemplary lists; and

FIG. 41 illustrates an example of normalized trajectory data.

DESCRIPTION OF EMBODIMENT

For example, an origin-destination (OD) search to retrieve a route froma specified origin to a specified destination from among a plurality oftrajectories of trajectory data acquired through actual observation isperformed. From a plurality of trajectories, the analysis of afrequently appearing OD representing the combination of an origin and adestination appearing a certain number of times (for example, ten times)or more, such as Shinjyuku station and Shibuya station, Shinagawastation and Ikebukuro station, or the like, is performed. From amongtrajectories, a partial route search such as retrieving a route, forexample, Shinagawa station→(Yamanote-line clockwise)→Ikebukuro stationis performed. From trajectories, the analysis of a frequently appearingpartial route representing a partial route appearing a certain number oftimes (for example, ten times) or more is performed.

Trajectory data representing trajectories used for route analysisinclude errors and are acquired at different observation times, andtherefore it is difficult to use the trajectory data for route analysisas they are. As an initial process for route analysis, for example, eachtrajectory is associated with a simple route graph obtained byintegrating a plurality of trajectories.

For example, the matching to the route graph is performed using a graphsearch algorithm. The matching is performed so that the minimum sum ofthe distances between an observation point on the trajectory and a linkon the route graph is obtained.

As a similarity degree between the route graph and the trajectory, aFrechet distance is used, and a path having a similarity level degree toor greater than a threshold is extracted from the route graph as a pathcorresponding to the trajectory.

For example, in a case where the matching is performed so that theminimum sum of the distances between an observation point on thetrajectory and a link on the route graph is obtained, the estimation ofa distance may not be correctly performed if the trajectory includes aU-turn or a loop where the direction of movement changes.

In a case where a Frechet distance is used as a similarity degreebetween a trajectory and a route graph, the direction of movement istaken into consideration. For example, in a case where a Frechetdistance is used, a path having the highest similarity degree may not beextracted when extracting a path having a similarity degree equal to orgreater than a threshold with respect to a trajectory. Accordingly, analgorithm for extracting a path having a similarity degree equal to orgreater than a threshold is repeatedly used to extract a path having thehighest similarity degree. In order to extract a path having the highestsimilarity degree, the calculation of similarity degrees of all pathsincluded in the route graph may be performed in a round-robin manner.

FIG. 1 illustrates an example of a route information processing system.An route information processing apparatus 10 illustrated in FIG. 1 isincluded in a route information processing system 20 along with atrajectory data generation apparatus 22, a trajectory data storage unit24, and a route graph storage unit 25.

The trajectory data generation apparatus 22 acquires, via a network 28,observation data representing the position of a movable bodyperiodically observed by each sensor 26 that observes the position ofthe movable body. The sensor 26 may be the Global Positioning System(GPS) or the like used by a terminal such as a mobile phone or asmartphone held by a person that represents an example of a movablebody, a car navigation system in a vehicle that represents an example ofa movable body or the like. The observation data include location datarepresented by the latitude and longitude of each observation point, anobservation time, and a sensor ID to identify the sensor 26. Thetrajectory data generation apparatus 22 classifies the acquiredobservation data according to sensor ID, and chronologically arrangeslocation data included in each of observation data based on observationtime to generate trajectory data. The trajectory data specifies atrajectory along which a movable body has moved. The trajectory datageneration apparatus 22 stores the generated trajectory data in thetrajectory data storage unit 24.

FIG. 2 illustrates an example of trajectory data. For example, asillustrated in FIG. 2, in the trajectory data storage unit 24, theidentifier of the trajectory data (a trajectory ID, for example, asensor ID), the identifier of each observation point (an observationpoint ID) included in the trajectory, and the x coordinate and ycoordinate of each observation point are associated with one another andstored. The x coordinate and the y coordinate are, for example, alatitude and a longitude, respectively.

The route graph storage unit 25 stores a route graph. A route graph isgenerated by integrating a plurality of trajectories and is representedby a plurality of nodes and links between nodes. FIG. 3 illustrates anexample of a route graph. For example, as illustrated in FIG. 3, theroute graph storage unit 25 stores the identifier of each node (a nodeID) and the x coordinate and y coordinate of each node which areassociated with each other, and further stores link information.Referring to FIG. 3, the link information is represented in a format inwhich the node IDs of nodes at both ends of a link are coupled by anunderscore (“_”). In the following description, an observation pointhaving the observation point ID of i may be represented as an“observation point i”, and a node having the node ID of X may berepresented as a “node X”.

The trajectory data storage unit 24 may be a storage device included inthe trajectory data generation apparatus 22 or may be provided as anexternal apparatus different from the trajectory data generationapparatus 22. Each of the trajectory data storage unit 24 and the routegraph storage unit 25 may be a portable storage medium such as a compactdisc read-only memory (CD-ROM), a digital versatile disc read-onlymemory (DVD-ROM), or a Universal Serial Bus (USB) memory.

As illustrated in FIG. 1, the route information processing apparatus 10includes an acquisition unit 11, a calculation unit 12, and anextraction unit 13.

The acquisition unit 11 acquires single trajectory data to be subjectedto normalization from the trajectory data storage unit 24 using atrajectory ID. The acquisition unit 11 acquires a route graph from theroute graph storage unit 25. The whole route graph or a part route graphincluding the trajectory data to be subjected to normalization may beacquired.

FIG. 4 illustrates an example of a trajectory and an example of a routegraph. FIG. 4 illustrates a trajectory represented by trajectory dataand a route graph that are acquired by the acquisition unit 11. In FIG.4, each observation point on the trajectory is represented by anobservation point ID in a rectangular box, and the observation pointsthat are chronologically arranged are coupled by a solid line segment.Each node on the route graph is represented by a node ID in a circle,and each link between the nodes is represented by a broken line. In thefollowing drawings, the same method of representing a trajectory and aroute graph may be employed. The observation points in the trajectorydata are assigned with observation point IDs=1, 2, . . . inchronological order. The order of nodes on a route graph may bedetermined based on link information between nodes and node IDs. Forexample, in FIG. 4, the nodes on the route graph may be arranged in theorder of A→B→C→D→E→F.

The calculation unit 12 calculates the similarity degree between a linesegment between observation points on a trajectory and a pathrepresented by the series of nodes corresponding to the line segment.

As a similarity degree in consideration of the direction of movement ofa movable body represented by a trajectory, a Frechet distance is used.The Frechet distance may be the maximum value of a distance betweencorresponding points where a trajectory and a route graph are associatedwith each other. A path on a route graph which has the shortest Frechetdistance to a trajectory is extracted as a normalized trajectory using agraph search algorithm. The normalization of a trajectory is efficientlyperformed in consideration of the direction of movement.

FIGS. 5, 6A, and 6B illustrate an example of a correspondence between aline segment between observation points on a trajectory and a node on aroute graph. For example, as illustrated in FIG. 5, in a case where theone-to-one correspondence is found between a line segment betweenobservation points on a trajectory and a node on a route graph, thedistance between the line segment and the node, which is nearest to theline segment, may be calculated. For example, as illustrated in FIGS. 6Aand 6B, in a case where a plurality of nodes correspond to a single linesegment, a calculation cost may be high. For example, the nodecorresponding to the line segment may be a node located within a certaindistance of the line segment. The distance between a trajectory and aroute graph may be obtained by calculating the distance between a linkon the route graph and a corresponding observation point on thetrajectory. In this case also, in a case where a plurality ofobservation points correspond to a single link, a calculation cost maybe high.

In a case where a plurality of nodes correspond to a single linesegment, it may be difficult to extract a path accurately reflecting atrajectory if the nodes are not associated with the line segment incorrect order. For example, in a case where the correspondence between aline segment and each node is established using a perpendicular lineextending from the node to the line segment so that the shortestdistance between the node and the line segment is achieved, points onthe line segment corresponding to the nodes may be arranged in the orderof A→C→B→D, which may be different from the original order of A→B→C→D asillustrated in FIG. 6A. In order to keep the original node order ofA→B→C→D, the correspondence between a line segment and each node may beestablished in consideration of the order of the nodes as illustrated inFIG. 6B.

FIG. 7 illustrates an example of a correspondence between a line segmentbetween observation points on a trajectory and a node on a route graphat the time of updating. As illustrated in FIG. 7, in a case where apath corresponding to a trajectory is updated while searching for anadjacent node, the correspondence may be changed. In FIG. 7, a point onthe line segment between an observation point 1 and an observation point2 (a line segment between an observation point i and an observationpoint (i+1) is hereinafter referred to as a “line segment i_i+1)corresponding to a node B is changed each time node searching isperformed, such as the node B, . . . , a node D, . . . , and a node F.Each time the point is changed, the distance between the node and theline segment is recalculated, which may lead to an increase incalculation cost.

The calculation unit 12 does not determine a point on a line segment ina trajectory which corresponds to a node on a route graph, andcalculates the distance between the line segment and the correspondingnode. In a case where a plurality of nodes correspond to a line segment,the calculation unit 12 calculates the Frechet distance between each setof two of the plurality of nodes and the line segment and sets one ofthe calculated Frechet distances which has the maximum value as thesimilarity degree between the line segment and a path including thenodes corresponding to the line segment.

For example, a Frechet distance ε₀ between a trajectory (the observationpoints 1 and 2) and a route graph (path: nodes A→B→C→D→E→F), which areillustrated in FIG. 4, is calculated. For example, the nodes A, B, C, D,E, and F correspond to a line segment 1_2.

One node in the set of two nodes is defined as a node X, and the otherone node is defined as a node Y. One of the Frechet distance between theline segment 1_2 and the node X and the Frechet distance between theline segment 1_2 and the node Y which has a larger value is defined asε_(X, Y). The calculation unit 12 calculates the Frechet distanceε_(X, Y) for each set of the node X and the node Y. FIG. 8 illustratesan example of a matrix. The matrix illustrated in FIG. 8 is used for thecalculation of the Frechet distance ε_(X, Y) between a line segment anda set of two nodes. As illustrated in FIG. 8, the Frechet distancesε_(X, Y) of all sets of the node X and the node Y are recorded incorresponding cells in the matrix. The calculation unit 12 sets themaximum value of the Frechet distance ε_(X, Y) in the matrix, forexample, “42.4” in FIG. 8, as the Frechet distance ε₀ representing thesimilarity degree between the line segment 1_2 and the route graph.

The calculation unit 12 may calculate each Frechet distance ε_(X, Y) asfollows to take the order of nodes into account. FIG. 9 illustrates anexample of a shortest distance between a node and a line segment. Asillustrated in FIG. 9, the shortest distance between each node and theline segment is calculated. In a case where the foot of a perpendicularline dropped from a node to the line segment is included in the linesegment, the length of the perpendicular line may be the shortestdistance. In a case where the foot of a perpendicular line dropped froma node to the line segment is not included in the line segment, thedistance between the node and one of observation points nearer to thenode may be the shortest distance. The foot of a perpendicular linedropped from a node X or one of observation points nearer to the node Xis defined as I_(X), and the shortest distance between the node X andthe line segment is defined as d(X, I_(X)). The foot of a perpendicularline dropped from a node Y or one of observation points nearer to thenode Y is defined as I_(Y), and the shortest distance between the node Yand the line segment is defined as d(Y, I_(Y)). In a case where I_(X)and I_(Y) are arranged in the same order in which corresponding nodesare arranged, one of d(X, I_(X)) and d(Y, I_(Y)) having a larger valueis set as the Frechet distance ε_(X, Y). For example, in a case wherethe nodes X and Y are arranged in this order and I_(X) is nearer to theobservation point 1 on the line segment 1_2 than I_(Y), I_(X) and I_(Y)may be determined to be arranged in the same order in which the nodes Xand Y are arranged.

FIGS. 10A, 10B, and 10C illustrate an example of a method of calculatinga Frechet distance. FIGS. 10A, 10B, and 10C illustrate a method ofcalculating the Frechet distance ε_(X, Y) in a case where the order ofnodes is reversed. In a case where I_(X) and I_(Y) are not arranged inthe same order as the corresponding nodes arranged, the calculation unit12 calculates a distance ε_(X, Y) _(_) ₁ from the intersection of aperpendicular bisector of a line segment between the two nodes and theline segment to the node X or Y as illustrated in FIG. 10A. Thecalculation unit 12 calculates a distance ε_(X, Y) _(_) ₂ that is thelonger one of the distance between I_(X) and the node X and the distancebetween I_(X) and the node Y as illustrated in FIG. 10B. The calculationunit 12 calculates a distance ε_(X, Y) _(_) ₃ that is the longer one ofthe distance between I_(Y) and the node X and the distance between I_(Y)and the node Y as illustrated in FIG. 10C. The calculation unit 12 setsthe shortest one of the distance ε_(X, Y) _(_) ₁, the distance E_(m-2),and the distance ε_(X, Y) _(_) ₃ as the Frechet distance ε_(X, Y).

All of the distance ε_(X, Y) _(_) ₁, the distance ε_(X, Y) _(_) ₂, andthe distance ε_(X, Y) _(_) ₃ may be calculated and compared with oneanother, or the Frechet distance ε_(X, Y) may be calculated according toa case as follows. d(X, I_(X)) and d(Y, I_(Y)) are calculated. In thecase of d(X, I_(X))≧d(Y, I_(Y)), d(X, I_(X)) is set as the Frechetdistance ε_(X, Y). In the case of d(X, I_(X))<d(Y, I_(Y)), d(Y, I_(Y))is set as the Frechet distance ε_(X, Y). In the other cases, thedistance ε_(X, Y) _(_) ₁ is set as the Frechet distance ε_(X, Y).

FIG. 11 illustrates an example of a method of calculating a Frechetdistance. FIG. 11 illustrates the calculation of the Frechet distanceε_(X, Y) between a line segment and two nodes at the time of updating.In a case where the calculation unit 12 updates a path whilesequentially searching for a node adjacent to a node included in theextracted path, the calculation unit 12 calculates the Frechet distanceε_(X, Y) of a set of newly retrieved nodes as illustrated in FIG. 11.The calculation unit 12 compares the maximum value of the Frechetdistance ε_(X, Y) calculated before the updating, for example, a valuein a thick-line frame in each matrix illustrated in FIG. 11, with eachof newly calculated Frechet distances ε_(X, Y). The maximum value of theFrechet distance ε_(X, Y) is set as the Frechet distance ε₀ representingthe similarity degree between a trajectory and a route graph.

The extraction unit 13 extracts a path corresponding to a trajectory sothat the similarity degree with respect to each line segment included inthe trajectory, which has been calculated by the calculation unit 12, ismaximized, for example, the Frechet distance ε₀ is minimized. Theextraction unit 13 outputs the coordinates of each node included in theextracted path and link information as normalized trajectory data.

FIG. 12 illustrates an example of a computer. The route informationprocessing apparatus 10 may be realized by, for example, a computer 40illustrated in FIG. 12. The computer 40 includes a CPU 41, a memory 42as a temporary storage, and a nonvolatile storage device 43. Thecomputer 40 further includes an input-output interface (I/F) 44 to whichan input-output device 48 is coupled. The computer 40 further includes aread/write (R/W) unit 45 for controlling reading and writing of datafrom and to a recording medium 49 and a network I/F 46 coupled to anetwork such as the Internet. The CPU 41, the memory 42, the storagedevice 43, the input-output I/F 44, the R/W unit 45, and the network I/F46 are coupled to one another via a bus 47.

The storage device 43 may be a hard disk drive (HDD), a solid statedrive (SSD), or a flash memory. The storage device 43 functioning as astorage medium stores a route information processing program 50 forcausing the computer 40 to function as the route information processingapparatus 10.

The CPU 41 reads the route information processing program 50 from thestorage device 43, decompresses the route information processing program50 in the memory 42, and sequentially executes processes included in theroute information processing program 50. The route informationprocessing program 50 includes an acquisition process 51, a calculationprocess 52, and an extraction process 53.

The CPU 41 may operate as the acquisition unit 11 illustrated in FIG. 1by executing the acquisition process 51. The CPU 41 may operate as thecalculation unit 12 illustrated in FIG. 1 by executing the calculationprocess 52. The CPU 41 may operate as the extraction unit 13 illustratedin FIG. 1 by executing the extraction process 53. The computer 40 thatexecutes the route information processing program 50 functions as theroute information processing apparatus 10.

The route information processing apparatus 10 may be realized by, forexample, a semiconductor integrated circuit such as an applicationspecific integrated circuit (ASIC).

FIG. 13 illustrates an example of a route information process. FIG. 14illustrates an example of trajectory and an example of a route graph.FIG. 15 illustrates an example of exemplary a number of a line segment.The trajectory data generation apparatus 22 acquires observation dataacquired by each of the sensors 26 via the network 28, generatestrajectory data from the observation data, and stores the trajectorydata in the trajectory data storage unit 24. A route graph is stored inthe route graph storage unit 25 in advance. In this state, the routeinformation processing apparatus 10 executes a route informationprocessing routine illustrated in FIG. 13. The route informationprocessing routine executed by the route information processingapparatus 10 may be an example of a route information processing method.

In operation S10 in the route information process illustrated in FIG.13, the acquisition unit 11 acquires a route graph from the route graphstorage unit 25 and acquires trajectory data to be normalized from thetrajectory data storage unit 24. FIG. 14 illustrates an example of atrajectory and an example of a route graph. For example, the route graphand the trajectory data illustrated in FIG. 14 may be acquired.

In operation S11, the extraction unit 13 extracts all nodes within adistance c from a starting point of a trajectory, for example, anobservation point 1 illustrated in FIG. 14, and sets a node set {V} ofthe nodes. The distance c is to determine a node corresponding to a linesegment between observation points, and may be, for example, ε=50.{V}={A, C} is set.

In operation S12, the extraction unit 13 selects a node V from the nodeset {V}. For example, a node A may be selected.

In operation S13, the extraction unit 13 sets target processing data (d,−i, V, V′, S, path). d represents a Frechet distance ε−₀ between aretrieved line segment and a path. i represents a number to identify theline segment between observation points and indicates how far the linesegment corresponding to the node V has been searched. As illustrated inFIG. 15, line segments including a virtual line segment set before thestarting point of the trajectory and a virtual line segment set afterthe end point of the trajectory are sequentially assigned numbers i=0,1, 2, . . . . V represents a retrieved node, V′ represents a node thatis adjacent to the node V and is being retrieved. S represents thearrangement of nodes corresponding to an ith line segment (taking theorder of the nodes into account). “path” represents a retrieved path.Operation S13 is at the start of retrieval, d=0, i=0, V′=V, S=[ ](empty), and path 32 [ ] are set as initial values.

FIG. 16 illustrates an example of a calculation process. In operationS14, the calculation unit 12 performs the distance calculation processillustrated in FIG. 16. In order to differentiate the distancecalculation process performed in operation S14 from a distancecalculation process performed in operation S22, the distance calculationprocess performed in operation S14 may be referred to as “initialdistance calculation process”. The distance calculation processperformed in operation S22 may be referred to as “second-stage distancecalculation process”.

FIGS. 17, 18, and 19 illustrate an example of an initial distancecalculation process. FIG. 17 illustrates details of the initial distancecalculation process performed at the current setting. In FIG. 17,“target processing data” corresponds to (d, −i, V, V′, S, path) set inoperation S13.

In operation S31 in FIG. 16, the calculation unit 12 sets the larger oneof i and 1 to a variable j representing the number of a line segmentbeing retrieved as a line segment corresponding to a node V′. Forexample, since i=0 is set, j=1 is set. The calculation unit 12 setsS+[V′] to S′ representing the arrangement of nodes corresponding to ajth line segment. For example, S′=[A] is set. The calculation unit 12sets path+[V′] to path′ representing a path to which a retrieved nodehas been newly added. For example, path′=[A] is set. The calculationunit 12 sets 0 as an initial value of a distance d1 between anobservation point j and a link V_V′. Values set in operation S31 arevalues of “j”, “S′”, “path′”, and “d1” in <d′> in FIG. 17.

In operation S32, the calculation unit 12 calculates a maximum value d1′of the distance between each of observation points j′ and j, for each j′where i+1≦j′≦j is established, and a link V_V′. The calculation of thedistance is performed in the procedure for calculating the Frechetdistance ε_(X, Y) using the matrix of <d1′> in FIG. 17. For example,since j′=1 is set, the distance of 10.0 between an observation point 1and a link A_A (=a node A) is d1′. The calculation unit 12 sets thelarger one of d1′ and d1 as d1. Since d1=0 is set in operation S31,d1=10.0 is set (see the upper part of FIG. 17). Since j′≧i+1 is set, thedistance calculation may be performed only for a set of observationpoints included in a newly searched line segment. d1 calculated inoperation S32 corresponds to the item of “d1” in <d′> in FIG. 17.

In operation S33, the calculation unit 12 determines whether d1calculated in operation S32 is equal to or less than ε. When d1 is equalto or less than ε, the node being retrieved is determined to be a nodecorresponding to the jth line segment and the process proceeds tooperation S34. When d1 is greater than ε, the node being retrieved isdetermined not to be a node corresponding to the jth line segment andthe process returns to the route information process illustrated in FIG.13. For example, since d1=10.0≦ε=50 is set, the determination is YES andthe process proceeds to operation S34.

In operation S34, the calculation unit 12 calculates d2 that is themaximum value of a distance d2′ between a node V″ and a node V′ and thejth line segment (line segment j_j+1) for each node V″ included in S′(see the upper part of FIG. 17). The calculation of the distance isperformed in the procedure for calculating the Frechet distance ε_(X, Y)using the matrix of <d2′> in FIG. 17. For example, since node V″=nodeV′=node A is set, the distance of 10.0 between a line segment 1_2 andthe link A_A (=the node A) is d2. The calculation unit 12 sets thelargest one of d, d1, and d2 as d′. For example, d′=10.0 is set. d2 andd′ calculated in operation S34 correspond to the items of “d2” and “d′”,respectively, in <d′> in FIG. 17.

In operation S35, the calculation unit 12 determines whether d′calculated in operation S34 is equal to or less than ε. When d′ is equalto or less than ε, the node being retrieved is determined to be acandidate to be newly added to a path and the process proceeds tooperation S36. For example, since d′=10.0≦ε=50 is set, the determinationis YES and the process proceeds to operation S36.

In operation S36, it is determined whether the combination of V′ and jis included in a list L. The list L is a list that records a Frechetdistance d after the retrieval for the node V has been completed to ithline segments, and includes the items of “V”, “i”, and “d” asillustrated in <list L> in FIG. 17. In a case where the combination of Vand i that matches the combination of V′ and j is included in the listL, the process proceeds to operation S37 and in a case where thecombination of V and i is not included in the list L, the processproceeds to operation S38. Since the list L is empty at the initialstage, the determination is NO and the process proceeds to operationS38.

In operation S38, the calculation unit 12 records (V′, j, d′) in theitems of “V”, “i”, and “d” in the list L, respectively. The calculationunit 12 records information about a newly retrieved node in a list Qthat indicates information about a retrieved node. For example, the listQ includes the items of “d”, “−i”, “V”, “S”, and “path” as illustratedin <list Q> in FIG. 17. The calculation unit 12 records (d′, −j, V′, S′,path′) in corresponding items of the list Q.

In operation S39, the extraction unit 13 increments j by one and sets[V′] for S′. By setting [V′] for S′, the calculation of the distance isperformed only upon the node V′ in operation S34.

In operation S40, it is determined whether j is equal to or less than prepresenting the number of observation points in the trajectory. When jis equal to or less than p, the process returns to operation S32. When jis greater than p, the process returns to the route information processin FIG. 13. For example, since j=1≦p=4 is set, the determination is YESand the process returns to operation S32.

FIG. 18 illustrates the process from operation S32 performed at thecurrent setting. At this stage, <target processing data> is the same asthat in FIG. 17. In <d′>, 0 is set to “d”, 10.0 is set to “d1”, 2 is setto “j”, [A] is set to “S′”, and [A] is set to “path′”. By performing thesame process as above, d1=41.2 is obtained in operation S32 (see theupper part of FIG. 18), the determination is YES in operation S33, andd2=40.0 (see the upper part of FIG. 18) and d′=41.2 are obtained inoperation S34. The determination is YES in operation S35, thedetermination is NO in operation S36, and data is added to the list Land the list Q as illustrated in FIG. 18 in operation S38. The processreturns to operation S32 again via operations S39 and S40.

FIG. 19 illustrates the process from operation S32 performed at thecurrent setting. At this stage, <target processing data> is the same asthat in FIG. 17. In <d′>, 0 is set to “d”, 41.2 is set to “d1”, 3 is setto “j”, [A] is set to “S′”, and [A] is set to “path′”. By performing thesame process as above, d1=98.5 is obtained in operation S32 (see theupper part of FIG. 19). Therefore, in operation S33, the determinationis NO and the process returns to the route information process in FIG.13.

In operation S15 in FIG. 13, whether the extraction unit 13 has selectedall nodes included in the node set {V} extracted in operation S11 isdetermined. When there is an unselected node, the process returns tooperation S12 and when all nodes have already been selected, the processproceeds to operation S16. For example, since the node C is notselected, the process returns to operation S12. The extraction unit 13selects the node C, sets (0, 0, C, C, [ ], [ ]) to the target processingdata (d, −i, V, V′, S, path) in operation S13, and performs theabove-described initial distance calculation process.

When the initial distance calculation process for the node C has beencompleted, the determination is YES in operation S15 and the processproceeds to operation S16. FIG. 20 illustrates an example of a list Qand an example of a list L after an initial distance calculationprocess. FIG. 21 illustrates an example of extraction of targetprocessing data in a first loop.

In operation S16, the extraction unit 13 moves data in the list Q to alist P to empty the list Q as illustrated in FIG. 21. In operation S17,the extraction unit 13 determines whether the list P is empty, and whenthe list P is empty, the process proceeds to operation S25, when thelist P is not empty, the process proceeds to operation S18. For example,since the list P is not empty, the process proceeds to operation S18.

In operation S18, the extraction unit 13 sorts the list P in ascendingorder for the items of “d” and “−i”. The extraction unit 13 extracts thetop data (d, −i, V, S, path) of the list P as target processing data.Since the list P has been sorted in ascending order for the items of “d”and “−i”, the top data is data representing the minimum value of theFrechet distance, for example, the highest similarity degree between aretrieved line segment and a path. For example, (d, −i, V, S,path)=(10.0, −1, A, [A], [A]) is extracted. This data indicates that thefirst line segment (the line segment 1_2) has already been searched, aretrieved node is A, a node corresponding to the first line segment is[A], a retrieved path is [A], and the Frechet distance between the pathand the first line segment in a trajectory is 10.0.

In operation S19, the extraction unit 13 determines whether “i” in thetarget processing data extracted in operation S18 is the same as p. Inthe case of i=p, the process proceeds to operation S24. In the case ofi≠p, the process proceeds to operation S20. For example, since i=1≠p=4is set, the determination is NO and the process proceeds to operationS20.

In operation S20, the extraction unit 13 extracts all nodes adjacent tothe node V in the item of “V” in the target processing data and sets anode set {V′} of the extracted nodes. For example, since the node V isthe node A, {V′}={B, C} is set.

In operation S21, the extraction unit 13 selects one node V′ from thenode set {V′}. For example, a node B may be selected.

In operation S22, the extraction unit 13 performs the distancecalculation process illustrated in FIG. 16 as the second-stage distancecalculation process.

FIGS. 22, 23, and 24 illustrate an example of a second-stage distancecalculation process. FIG. 22 illustrates the second-stage distancecalculation process performed at the current setting. At this stage, in<target processing data>, the target processing data extracted inoperation S18 and the node V′ selected in operation S21 are set. Byperforming the same process as above, in <d′>, 1 is set to “j”, [AB] isset to “S′”, [AB] is set to “path′”, and 0 is set to “d1” in operationS31. In operation S32, because there is no j′ satisfying i+1≦j′≦j, d1=0is obtained (see <d1′> in FIG. 22). The determination is YES inoperation S33; in operation S34, d2=110 (see the upper part of FIG. 22)and d′=110 are obtained; in operation S35, the determination is NO; andthe process returns to operation S32 again via operations S39 and S40.

FIG. 23 illustrates the process from operation S32 performed at thecurrent setting. At this stage, <target processing data> is the same asthat in FIG. 22. In <d′>, 10.0 is set to “d”, 0 is set to “d1”, 2 is setto “j”, [B] is set to “S′”, and [AB] is set to “path′”. By performingthe same process as above, d1=41.2 is obtained (see the upper part ofFIG. 23) in operation S32, the determination is YES in operation S33,and d2=41.2 (see the upper part of FIG. 23) and d′=41.2 are obtained inoperation S34. In operation S35, the determination is YES; in operationS36, the determination is NO; and in operation S38, each item is addedin the list Q and the list L as illustrated in FIG. 23. The processreturns to operation S32 again via operations S39 and S40.

In the case of j=3, the process from operation S32 is also performed. Inoperation S38, (V, i, d)=(B, 3, 41.2) is added to the list L and (d, −i,V, S, path)=(41.2, −3, B, [B], [AB]) is added to the list Q. The processreturns to operation S32 again via operations S39 and S40.

In the case of j=4, d3=80 is obtained in operation S32, thedetermination is NO in operation S33, and the process returns to theroute information process illustrated in FIG. 13. The determination isNO in operation S23, and the process returns to operation S21. Inoperation S21, the extraction unit 13 selects a node C as the node V′,and in operation S22, the second-stage distance calculation process isperformed.

FIG. 24 illustrates the second-stage distance calculation process at thecurrent setting. At this stage, in <target processing data>, the targetprocessing data extracted in operation S18, (d, −i, V, S, path)=(10.0,−1, A, [A], [A]) is set and the node C selected in operation S21 is setas the node V′. By performing the same process as above, in operationS31, 1 is set to “j”, [AC] is set to “S′”, [AC] is set to “path′”, and 0is set to “d1′ in <d′>. In operation S32, there is no j′ satisfyingi+1≦j′≦j, d1=0 is obtained (see <d1′> in FIG. 24). The determination isYES in operation S33; in operation S34, d2=10.0 (see the upper part ofFIG. 24) and d′=10.0 are obtained; in operation S35, the determinationis YES; and the process proceeds to operation S36.

Since (V′, j)=(C, 1) is included in the list L, the determination is YESin operation S36 and the process proceeds to operation S37. In operationS37, the calculation unit 12 determines whether d′ calculated inoperation S34 is less than “d” corresponding to (V, i) that is the sameas the combination of (V′, j) included in the list L. For example, sinced′<d in the list L, the process proceeds to operation S38. In operationS38, as illustrated in FIG. 24, the calculation unit 12 updates dcorresponding to (V, i) that is the same as (V′, j) with d′ in the listL. The calculation unit 12 deletes (V, i) that is the same as (V′, j) inthe list P. The calculation unit 12 adds (d′, −j, V′, S′, path′) to thelist Q. The process returns to operation S32 again via operations S39and S40.

In the case of j=2, the process from operation S32 is also performed. Inoperation S34, d′=31.6 is obtained; in operation S35, the determinationis YES; in operation S36, the determination is YES; and the processproceeds to operation S37. For example, (V′, j)=(C, 2) is set and dcorresponding to (C, 2) is 31.6 in the list L. Accordingly, since d′<din the list L is not satisfied, operation S38 is skipped and the processproceeds to operation S39. The process returns to operation S32 againvia operations S39 and S40.

In the case of j=3, d1=94.9 is obtained in operation S32 and thedetermination is NO in operation S33. The process returns to the routeinformation process illustrated in FIG. 13. In operation S23, thedetermination is YES and the process returns to operation S16.

FIGS. 25 to 40 illustrate an example of a list. FIG. 25 illustrates thelist Q and the list L after the first loop (an nth loop is hereinafterreferred to as “loop n”) in the second-stage distance calculationprocess. The process from operation S16 to operation S23 may be one loopin the second-stage distance calculation process.

In FIG. 26, target processing data is extracted in a loop 2. In the loop2 in the second-stage distance calculation process, the extraction unit13 moves data in the list Q to the list P and empties the list Q in theprocess from operation S16 to operation S18 as illustrated in FIG. 26.The extraction unit 13 sorts the list P in “d” and “−i” and extracts thetop data, (d, −i, V, S, path)=(10.0, −1, C, [AC], [AC]), as targetprocessing data.

By performing the same process as above in the second-stage distancecalculation process (the loop 2), the list Q and the list L after thesecond-stage distance calculation process (the loop 2), illustrated inFIG. 27, are obtained. FIG. 28 illustrates the extraction of targetprocessing data in the second-stage distance calculation process (a loop3) and FIG. 29 illustrates the list Q and the list L obtained after thesecond-stage distance calculation process (the loop 3). Similarly, FIG.30 illustrates the extraction of target processing data in thesecond-stage distance calculation process (a loop 4). FIG. 31illustrates the extraction of target processing data in the second-stagedistance calculation process (a loop 5) and FIG. 32 illustrates the listQ and the list L obtained after the second-stage distance calculationprocess (the loop 5). FIG. 33 illustrates the extraction of targetprocessing data in the second-stage distance calculation process (a loop6) and FIG. 34 illustrates the list Q and the list L obtained after thesecond-stage distance calculation process (the loop 6). FIG. 35illustrates the extraction of target processing data in the second-stagedistance calculation process (a loop 7) and FIG. 36 illustrates the listQ and the list L obtained after the second-stage distance calculationprocess (the loop 7). FIG. 37 illustrates the extraction of targetprocessing data in the second-stage distance calculation process (a loop8). FIG. 38 illustrates the extraction of target processing data in thesecond-stage distance calculation process (a loop 9) and FIG. 39illustrates the list Q and the list L after the second-stage distancecalculation process (the loop 9). After the loop 4 and the loop 8, thelist Q and the list L may not be changed from those after the previousloop.

As illustrated in FIG. 40, in target processing data extracted in thesecond-stage distance calculation process (loop 10), i=p (=4) is set asillustrated in FIG. 40. Therefore, the determination is YES in operationS19 and the process proceeds to operation S24.

In operation S24, the extraction unit 13 extracts “path” in theextracted target processing data, for example, [ACIJ], as a normalizedtrajectory. For example, the trajectory (the observation points 1, 2, 3,and 4) illustrated in FIG. 14 indicates matching with a path of thenodes A→C→I→J on the route graph. FIG. 41 illustrates an example ofnormalized trajectory data. The extraction unit 13 outputs the extractedpath as normalized trajectory data as illustrated in, for example, FIG.41. The route information process ends.

In a case where it is determined in operation S17 that the list P isempty before the determination is YES in operation S19, a pathcorresponding to the trajectory may not exist in the route graph. Theprocess proceeds to operation S25, and the extraction unit 13 outputs anerror to end the route information process.

In a route information processing apparatus, the Frechet distance thatis the maximum value of the distance between each set of two nodesassociated with a line segment between observation points and the linesegment is calculated as the similarity degree between a trajectory anda path on the route graph. Accordingly, the similarity degree betweenthe trajectory and the path on the route graph may be efficientlycalculated. Since the Frechet distance where the order of nodes is takeninto account is calculated as the distance between a node and a linesegment, a similarity degree accurately reflecting a portion where thedirection of movement changes, for example, a U-turn or a loop includedin a trajectory, may be calculated.

In a case where a path that matches a trajectory is updated whilesearching for a node adjacent to an existing node, only for newlyretrieved nodes, the distance between each node of a set of nodes and aline segment may be calculated and a result of the calculation may becompared with the Frechet distance calculated before the updating. Thecost of calculation for the matching between the trajectory and the pathon a route graph may be therefore reduced.

The route information processing program 50 may be stored (installed) inthe storage device 43 in advance. The route information processingprogram 50 may be recorded in a recording medium such as a CD-ROM,DVD-ROM, USB memory, or the like and the recording medium recording theroute information processing program 50 may be provided.

All examples and conditional language recited herein are intended forpedagogical purposes to aid the reader in understanding the inventionand the concepts contributed by the inventor to furthering the art, andare to be construed as being without limitation to such specificallyrecited examples and conditions, nor does the organization of suchexamples in the specification relate to a showing of the superiority andinferiority of the invention. Although the embodiment of the presentinvention has been described in detail, it should be understood that thevarious changes, substitutions, and alterations could be made heretowithout departing from the spirit and scope of the invention.

What is claimed is:
 1. A route information processing apparatuscomprising: a processor configured to execute a program; and a memoryconfigured to store the program, wherein, based on the program, theprocessor performs operations to: calculate maximum values correspondingto a Frechet distance between one line segment of one or more linesegments between observation points, which are generated chronologicallyby that a movable body moves and included in a trajectory, and each ofsets of two nodes, which are included in fixed nodes, corresponding tothe one line segment based on a first order of the fixed nodes and asecond order of observation points generated chronologically, the fixednodes being included in a route graph including linked paths which linksnodes of the fixed nodes; and acquire a path corresponding to thetrajectory having a smallest value among the maximum values of the oneor more line segments.
 2. The route information processing apparatusaccording to claim 1, wherein the one or more line segments are set inthe second order of observation times at the observation points.
 3. Theroute information processing apparatus according to claim 1, wherein theprocessor, when the acquiring is performed while updating the path,calculates the maximum values based on new maximum values for a set oftwo newly retrieved nodes and previously-calculated maximum values. 4.The route information processing apparatus according to claim 1, whereinthe processor obtains a first position corresponding to a first distanceof a shortest distance from a first node of one of the sets to the oneline segment and a second position corresponding to a second distance ofa shortest distance from a second node of the one of the sets to the oneline segment.
 5. The route information processing apparatus according toclaim 4, wherein the processor calculates the maximum value based on arelationship among the first position, the second position, andpositions of the observation points corresponding to the one or moreline segment.
 6. The route information processing apparatus according toclaim 5, wherein, based on the relationship, the processor sets, as themaximum value, a longer one of the first distance and the seconddistance, or, sets, as the maximum value, a shortest one of the firstdistance, the second distance, and a third distance from an intersectionof a perpendicular bisector of a line segment between the first node andthe second node to the one line segment.
 7. The route informationprocessing apparatus according to claim 1, wherein the two nodescorresponding to the one line segment is located within a certaindistance of the one line segment.
 8. A route information processingmethod, comprising: calculating, by a computer, maximum valuescorresponding to a Frechet distance between one of one or more linesegments between observation points, which are generated chronologicallyby that a sensor observes a position of a movable body periodically andincluded in a trajectory, and each of sets of two nodes, which areincluded in fixed nodes, corresponding to the one line segment based ona first order of the fixed nodes and a second order of observationpoints generated chronologically, the fixed nodes and are included in aroute graph including linked paths which link nodes of the fixed nodes;and acquiring a path corresponding to the trajectory having a smallestvalue among the maximum values for each of the one or more linesegments.
 9. The route information processing method according to claim8, wherein the one or more line segments are set in the second order ofobservation times at the observation points.
 10. The route informationprocessing method according to claim 8 wherein, when the acquiring isperformed while updating the path, the maximum values are calculatedbased on new maximum values for a set of two newly retrieved nodes andpreviously-calculated maximum values.
 11. The route informationprocessing method according to claim 8, further comprising, obtaining afirst position corresponding to a first distance of a shortest distancefrom a first node of one of the sets to the one line segment and asecond position corresponding to a second distance of a shortestdistance from a second node of the one of the sets to the one linesegment.
 12. The route information processing method according to claim11, wherein the maximum values are calculated based on a relationshipamong the first position, the second position, and positions of theobservation points corresponding to the one or more line segment. 13.The route information processing apparatus according to claim 12,wherein, based on the relationship, a longer one of the first distanceand the second distance is set as the maximum value, or, a shortest oneof the first distance, the second distance, and a third distance from anintersection of a perpendicular bisector of a line segment between thefirst node and the second node to the one line segment is set as themaximum.
 14. The route information processing apparatus according toclaim 8, wherein the two nodes corresponding to the one line segment islocated within a certain distance of the one line segment.